First Step:

Create subdomain like “mg.example.com” through Cpanel

Second Step:

Create Email Account i.e “[email protected]” through Cpanel and note its password.

Third Step:

Login to Mailgun Add New Domain (i.e subdomain).
https://app.mailgun.com/app/sending/domains

Add SubDomain that created through Cpanel (i.e mg.example.com).

Fourth Step:

Login to CloudFlare and Search Specific site in Search box.

Next Click on DNS

Click on DNS taking screenshots of all setting and then Add TXT , CNAME and MX entries in CloudFlare DNS value taking from Mailgun where We add domain and click on Add Domain then generate TXT , CNAME , MX value.

Mailgun activation

Fifth Step:

Then Install Mailgun Plugin
https://wordpress.org/plugins/mailgun/

Mailgun Plugin Configuration setting
API Key taking from mailgun
https://app.mailgun.com/app/dashboard

Next Clicking On API Security

Copy The API Key

1-Enter Mailgun Domain Name: mg.example.com
2-Enter API Key.
3-Enter From Address (Email i.e [email protected])

NOTE : Test Contact Form wherever its implemented on site in Test mode, means change emails have a test screenshot and revert back Emails.